今天想要出道题，给感兴趣的同学做一下哈哈。

2021-01-16 本文已影响0人周橙哲博士

Let $f(x)=\frac{1}{\sqrt{3 x-6}},$ for $x>2 .$

(a) Find $\int(f(x))^{2} \mathrm{~d} x$ .

Part of the graph of $f(x)$ is shown in the following diagram.

image.png

The shaded region $R$ is enclosed by the graph of $f,$ the $x$ -axis, and the lines $x=3$ and $x=11$ .

(b) Find the exact volume of the solid formed when $R$ is rotated $360^{\circ}$ about the $x$ -axis.